diff --git a/src/fri/fri.cairo b/src/fri/fri.cairo
index e55ef361c..db957c969 100644
--- a/src/fri/fri.cairo
+++ b/src/fri/fri.cairo
@@ -140,7 +140,7 @@ fn fri_commit(
     }
 }
 
-fn fri_decommit_layers(
+fn fri_verify_layers(
     fri_group: Span<felt252>,
     n_layers: felt252,
     commitment: Span<TableCommitment>,
@@ -184,7 +184,7 @@ fn fri_decommit_layers(
 }
 
 // FRI protocol component decommitment.
-fn fri_decommit(
+fn fri_verify(
     queries: Span<felt252>,
     commitment: FriCommitment,
     decommitment: FriDecommitment,
@@ -200,8 +200,8 @@ fn fri_decommit(
     // Compute fri_group.
     let fri_group = get_fri_group();
 
-    // Decommit inner layers.
-    let last_queries = fri_decommit_layers(
+    // Verify inner layers.
+    let last_queries = fri_verify_layers(
         fri_group.span(),
         commitment.config.n_layers - 1,
         commitment.inner_layers,
diff --git a/src/fri/fri_first_layer.cairo b/src/fri/fri_first_layer.cairo
index 0253d56e0..7b7a625f0 100644
--- a/src/fri/fri_first_layer.cairo
+++ b/src/fri/fri_first_layer.cairo
@@ -5,7 +5,7 @@ use core::traits::TryInto;
 
 use cairo_verifier::common::math;
 use cairo_verifier::fri::fri_layer::FriLayerQuery;
-use cairo_verifier::FIELD_GENERATOR_INV;
+use cairo_verifier::FIELD_GENERATOR_INVERSE;
 
 fn gather_first_layer_queries(
     queries: Span<felt252>, evaluations: Span<felt252>, x_values: Span<felt252>
@@ -20,7 +20,7 @@ fn gather_first_layer_queries(
         }
 
         // Translate the coset to the homogenous group to have simple FRI equations.
-        let shifted_x_value = *(x_values.at(i)) * FIELD_GENERATOR_INV;
+        let shifted_x_value = *(x_values.at(i)) * FIELD_GENERATOR_INVERSE;
 
         fri_queries
             .append(
diff --git a/src/fri/fri_last_layer.cairo b/src/fri/fri_last_layer.cairo
index 7d7e768c3..316c78d6e 100644
--- a/src/fri/fri_last_layer.cairo
+++ b/src/fri/fri_last_layer.cairo
@@ -16,9 +16,9 @@ fn verify_last_layer(queries: Span<FriLayerQuery>, coefficients: Span<ChannelSen
             break;
         }
         let value = horner_eval::horner_eval(
-            coefficients, math::mul_inverse(*(queries.at(i)).x_inv_value)
+            coefficients, math::mul_inverse(*queries.at(i).x_inv_value)
         );
-        assert(value == *(queries.at(i)).y_value, '');
+        assert(value == *queries.at(i).y_value, '');
         i += 1;
     }
 }
diff --git a/src/fri/fri_layer.cairo b/src/fri/fri_layer.cairo
index fe4491304..9eb045456 100644
--- a/src/fri/fri_layer.cairo
+++ b/src/fri/fri_layer.cairo
@@ -58,7 +58,7 @@ fn compute_coset_elements(
             coset_x_inv = (*queries.at(i).x_inv_value) * (*fri_group.at(i + j));
             i += 1;
         } else {
-            coset_elements.append(*(sibling_witness.at(j)));
+            coset_elements.append(*sibling_witness.at(j));
             j += 1;
         }
 
diff --git a/src/lib.cairo b/src/lib.cairo
index d6e811a6c..8c165325a 100644
--- a/src/lib.cairo
+++ b/src/lib.cairo
@@ -1,5 +1,5 @@
 const FIELD_GENERATOR: felt252 = 3;
-const FIELD_GENERATOR_INV: felt252 =
+const FIELD_GENERATOR_INVERSE: felt252 =
     1206167596222043737899107594365023368541035738443865566657697352045290673494;
 
 mod channel;